Instead of deleting your profile photo, change it!
This article will walk you through the step-by-step process.
Access your Profile by clicking the “my profile” link in the left-hand navigational menu. Click once on your current profile picture to open the upload window.
Click the “Choose File” button which will allow you to browse your computer for a new photo. Remember, profile photos must be 225 X 225 pixels in size and must be a .jpeg, .jpg, or .png image file.
Once you have picked the new photo, click the “upload photo” button.
The platform will prompt you to confirm that you want to keep the new photo. Click the button.
And your new photo will appear in your profile.